Disclosed herein generally are methods and systems for nuclear magnetic resonance (NMR) logging of subterranean formations, especially those containing fuel hydrocarbons in liquid or gaseous form; water; or brine. The invention concerns a method and apparatus for inverting three-dimensional fluid property distribution from NMR log data, especially pulsed NMR log data.
As is well known the logging of subterranean formations represents an extremely important contribution to the search for and recovery of rock-borne hydrocarbons that provide overwhelmingly the most commonly exploited sources of energy and chemicals used by mankind.
NMR logging in general has been in use for some decades. So-called “pulsed” NMR logging has been in widespread use since the 1990's.
Broadly speaking in pulsed NMR logging a cylindrical logging tool is moved (supported e.g. on wireline, the nature of which is known to the person of skill in the art; or on drill pipe, the nature of which is also known to the person of skill in the art) along a borehole formed in a fluid-bearing formation. In some NMR logging tool designs the logging tool is periodically halted in the borehole and in some other designs the logging tool is capable of logging while it is moving.
The logging tool includes one or more magnets the purpose of which is to emit a static magnetic field B0 into the formation in which the logging tool is deployed. This aligns (polarizes) protons in fluid contained within pores in the formation from a random (resting) state to the direction of the imposed B0 magnetic field.
It takes a certain time for the protons to become aligned in this way following the application of the static magnetic field. This time is known as the longitudinal relaxation time, denoted T1. T1 is sometimes called the “spin-lattice” relaxation time.
Protons that are aligned to an imposed magnetic field will precess towards the un-polarized, random state if the field is removed.
Precession of the protons gives rise to a detectable, decaying magnetic field. One or more antennae in the logging tool detect the decaying magnetic field, which is related to the T1 time by a known expression. The antennae generate signals indicative of the detected magnetic field values. It is possible to calculate T1 values based on the signals detected as a result of the decaying magnetic fields caused by precession of the protons.
T1 is a useful quantity that may be regarded as indicating the ease with which the protons become aligned in the static magnetic field. Thus T1 is in part indicative of the extent to which the protons interact with the boundaries of pores in the formation. In turn this can provide indications of the sizes of the pores. T1 also can be used to derive a measure of the viscosity of fluids contained within the pores.
The logging tool also generates timed bursts (pulse sequences) of radio frequency (RF) energy that give rise to an oscillating magnetic field B1. This tilts the aligned protons perpendicular to the direction of the applied magnetic field and causes them to precess in phase to one another. This phenomenon is referred to as nuclear magnetic resonance.
The duration and profile of the B1 field bursts are carefully controlled. When a B1 burst ends the logging tool antennae detect a signal, sometimes referred to as an echo, and generate an NMR signal indicative thereof. The time taken for the aforesaid signal to decay is referred to as the transverse relaxation time, denoted T2.
T2 is sometimes referred to as the “spin-spin” relaxation time. In practice in a logging tool a multi-stage burst is used because this tends to provide a series of readily detectable signal peaks (referred to as an “echo train”) from which the T2 amplitude may be calculated. In particular an initial RF emission that causes tilting of the spin axes of the protons by π/2 degrees is followed by a series of emissions that cause tilting by π degrees. The decay following the latter is detectable and is measured by the logging tool in order to generate a series of signal amplitude peaks from which the value of T2 can be derived.
The transverse relaxation time T2 while typically of shorter duration than the longitudinal relaxation time T1 also can be used to derive pore size information and information on pore fluid characteristics such as viscosity. The amplitude of the T1 and T2 relaxation time signals can be employed to derive a measure of the porosity of the formation.
The measurements taken using an NMR logging tool also can give rise to a coefficient of molecular diffusion (D) that in turn is useful in characterising the hydrocarbon-bearing fluids in the pores in the formation.
Use of an NMR logging tool therefore in theory can give rise to a three-dimensional dataset consisting of values related to T1, T2 and D. Such a dataset may be known as a three-dimensional kernel matrix where each entry corresponds to an NMR signal contribution from a unit of porosity for a specified (T1, T2, D) value tuple associated with a said entry. The signal contributions may be computed from fundamental equations that are well-known in the art.
The process of converting signal amplitude data generated in a logging tool into meaningful information that can be interpreted by a geoscientist or log analyst is sometimes referred to as “inversion”. In many cases an aim of inversion is to uncover unknown physical properties from associated measurements. In the case of pulsed NMR interpretation, the goal of inversion is to find the fluid property distribution over the domain of (T1, T2, D) given the measured NMR log and knowing the underlying 3D kernel matrix.
Up to the present time it has not been possible to perform inversion on the full three-dimensional matrix in an acceptable timescale, that is a timescale that is regarded as desirable in downhole situations. Until now it has on the contrary been necessary to process 3D NMR signal contributions “offline”, using inefficient non-linear optimisation techniques.
For reasons associated with the character of the fluids undergoing assessment it is however desirable to analyse NMR log data in real-time or near real-time (i.e. a relatively short time after the data have been generated).
Early in the development of pulsed NMR logging the computing power available either in on-board processing devices installed in the NMR logging tools, or in computers at surface locations and in communication with the logging tools, was not adequate to allow the inversion of large amounts of log data in real-time.
As a result geoscientists have historically confined themselves to inverting either the two-dimensional matrix constituted by the T1 and T2 data or the two-dimensional matrix constituted by the T2 and D data, at least when wishing to process the data in real-time or near real-time.
More recently the ability of portable computers to resolve complex inversion problems has improved significantly. However real-time or near-real-time inversion of NMR measurements from three-dimensional kernel matrix has hitherto remained unattempted. Furthermore, characterization of inversion uncertainty due to the underdetermined nature of the NMR inversion problem has also remained unaddressed until now.
U.S. Pat. No. 5,517,115 to Prammer teaches an NMR data analysis technique in which a priori information about the likely nature of an NMR signal is modeled in advance of NMR logging activity. The modeled information is used in a constrained selection to approximate fluid properties from two-dimensional NMR log data.
Publication US 2013/0080058 discloses a method of processing log data obtained from three mutually orthogonal logging tool antennae but does not discuss the solution of NMR log inversion problems.
“A global inversion method for multi-dimensional NMR logging” [Sun et al, Journal of Magnetic Resonance 172 (2005) 152-160] describes an inversion technique for multi-dimensional NMR log information. This publication teaches the solving of a composite three-dimensional kernel that models the magnitude of NMR echoes detected by a logging tool.
U.S. Pat. No. 6,960,913 to Heaton contains a historical survey of single value decomposition (SVD) techniques for analysing NMR log data. The method claimed in U.S. Pat. No. 6,960,913 is stated to be independent of prior knowledge of fluid sample properties.
U.S. Pat. No. 6,937,014 to Sun et al discloses a method for obtaining a multi-dimensional proton density from a system of nuclear spins.
Other publications believed to be of background relevance to the field of the invention include U.S. Pat. Nos. 7,034,528, 7,388,374, 7,538,547, 7,565,833, 8,044,662, 8,633,691, 8,643,363 and 8,736,263 together with “A new inversion method for (T2, D) 2D NMR logging and fluid typing” [Tan et al, Computers and Geosciences 51 (2013) 366-380].
An aim of the invention is to solve or at least ameliorate one or more problems of prior art logging tools and associated methods of the kinds described herein.